A method and device for machining rotationally symmetrical surfaces of a workpiece are known from DE 10 2004 026 675 B3, wherein the workpiece is rotatively driven to effect the cutting motion, and a tool with a cutting edge is moved relative to the workpiece with a feed motion such that the point of action between the cutting edge and the workpiece travels along the cutting edge. For this purpose, the cutting edge has the form of a helical line that extends coaxially to the rotational axis of the tool and is moved about the rotational axis of the tool with an arc-shaped feed motion. This makes it possible to produce unrifled surfaces with high cutting efficiency. However, the manufacture of such tools is relatively complicated due to the complex cutting edge geometry and is associated with correspondingly high costs. The re-sharpening, as well as other measures for preserving the cutting ability of such tools, are also more expensive.